Systems and Methods for Sync Mark Detection Metric Computation

ABSTRACT

Various embodiments of the present invention provide systems and methods for data processing. As an example, a pattern detection circuit is discussed that includes a distance calculation circuit and a comparator circuit. The distance calculation circuit is operable to calculate a noise whitened distance between a reference signal and a received input to yield a comparison value. The comparator circuit is operable to compare the comparison value with a threshold value.

BACKGROUND OF THE INVENTION

The present inventions are related to systems and methods for dataprocessing, and more particularly to systems and methods for detectingpatterns in a data stream.

Various circuits have been developed that provide for identifyingsynchronization marks within a data stream. As an example, asynchronization mark may be identified by calculating a Euclideandistance between a data set and a reference signal. The calculatedEuclidean distance is then compared to a threshold value. Where theEuclidean distance is found to be less than the threshold value, a syncmark is said to have been found. In some cases, a sync mark may beimproperly indicated or a sync mark may be missed due to noise.

Hence, for at least the aforementioned reasons, there exists a need inthe art for advanced systems and methods for sync mark identification.

BRIEF SUMMARY OF THE INVENTION

The present inventions are related to systems and methods for dataprocessing, and more particularly to systems and methods for detectingpatterns in a data stream.

Various embodiments of the present invention provide pattern detectioncircuits that include a distance calculation circuit and a comparatorcircuit. The distance calculation circuit is operable to calculate anoise whitened distance between a reference signal and a received inputto yield a comparison value. The comparator circuit is operable tocompare the comparison value with a threshold value. In some instancesof the aforementioned embodiments, the comparator circuit is furtheroperable to assert a pattern found signal when the comparison value isless than the threshold value.

In various instances of the aforementioned embodiments, the distancecalculation circuit includes: a difference circuit, a noise whiteningfilter and a multiplier circuit. The difference circuit is operable tocalculate a difference between the reference signal and the receivedinput at a bit position to yield a difference value. The noise whiteningfilter is operable to noise whiten the difference value to yield a noisewhitened output. The multiplier circuit is operable to square the noisewhitened output to yield a squared output. In some cases, the bitposition is a first bit position, the difference value is a firstdifference value, the noise whitened output is a first noise whitenedoutput, and the squared output is a first squared output. In such cases,the difference circuit is further operable to calculate a differencebetween the reference signal and the received input at a second bitposition to yield a second difference value; the noise whitening filteris further operable to noise whiten the second difference value to yielda second noise whitened output; the multiplier circuit is operable tosquare the second noise whitened output to yield a second squaredoutput; and an accumulator circuit operable to sum at least the firstsquared output and the second squared output to yield the comparisonvalue.

In one or more instances of the aforementioned embodiments, the circuitfurther includes a pattern register operable to maintain the referencesignal. In particular cases, the pattern register is programmable. Insome instances of the aforementioned embodiments, the comparison valueis calculated in accordance with the following equation:

${\text{comparison~~output} = {\sum\limits_{i = 0}^{l}\left\lbrack {\sum\limits_{k = 0}^{m}{f_{k}\left( {{{received}\mspace{14mu} {input}_{i - k}} - {{reference}\mspace{14mu} {signal}_{i - k}}} \right)}} \right\rbrack^{2}}},$

wherein l corresponds to the number of bit positions of the referencesignal, m corresponds to the number of taps of a noise whitening filter,i-k corresponds to a particular bit position, and f_(k) represents aparticular tap of the noise whitening filter.

Other embodiments of the present invention provide methods for patterndetection. Such methods include: receiving a data input; receiving areference signal; calculating a difference between the reference signaland the received input at a bit position to yield a difference value;noise whitening the difference value to yield a noise whitened output;and calculating a distance between the data input and the referencesignal based at least in part on the noise whitened output to yield acomparison value. In some instances, calculating the distance betweenthe data input and the reference signal based at least in part on thenoise whitened output includes squaring the noise whitened output toyield a squared output, wherein the comparison value is calculated basedat least in part on the squared output. In various instances, the bitposition is a first bit position, the difference value is a firstdifference value, the noise whitened output is a first noise whitenedoutput. In such instances, the methods further include: calculating adifference between the reference signal and the received input at asecond bit position to yield a second difference value; noise whiteningthe second difference value to yield a second noise whitened output;squaring the first noise whitened output to yield a first squaredoutput; squaring the second noise whitened output to yield a secondsquared output; and summing at least the first squared output and thesecond squared output to yield the comparison value.

Yet other embodiments of the present invention provide storage devices.Such storage devices include: a storage medium; a read/write headassembly disposed in relation to the storage medium and operable toderive a data input from the storage medium; an analog to digitalconverter circuit operable to convert the data input to a series ofdigital samples; an equalizer circuit operable to equalize the series ofdata samples to yield an equalized output; a distance calculationcircuit operable to calculate a noise whitened distance between areference signal and the equalized output to yield a comparison value;and a comparator circuit operable to compare the comparison value with athreshold value.

This summary provides only a general outline of some embodiments of theinvention. Many other objects, features, advantages and otherembodiments of the invention will become more fully apparent from thefollowing detailed description, the appended claims and the accompanyingdrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

A further understanding of the various embodiments of the presentinvention may be realized by reference to the figures which aredescribed in remaining portions of the specification. In the figures,like reference numerals are used throughout several figures to refer tosimilar components. In some instances, a sub-label consisting of a lowercase letter is associated with a reference numeral to denote one ofmultiple similar components. When reference is made to a referencenumeral without specification to an existing sub-label, it is intendedto refer to all such multiple similar components.

FIG. 1 is a block diagram of a known magnetic storage medium and sectordata scheme;

FIG. 2 a depicts a noise whitened based pattern detector circuit inaccordance with one or more embodiments of the present invention;

FIG. 2 b shows one implementation of a noise whitened distancecalculation circuit in accordance with some embodiments of the presentinvention;

FIG. 3 depicts a method in accordance with one or more embodiments ofthe present invention for identifying a pattern;

FIG. 4 depicts a communication system including a noise whitened basedpattern detector circuit in accordance with different embodiments of thepresent invention; and

FIG. 5 shows a storage system including a noise whitened based patterndetector circuit in accordance with some embodiments of the presentinvention.

DETAILED DESCRIPTION OF THE INVENTION

The present inventions are related to systems and methods for dataprocessing, and more particularly to systems and methods for detectingpatterns in a data stream.

Turning to FIG. 1, a storage medium 1 is shown with two exemplary tracks20, 22 indicated as dashed lines. The tracks are segregated by servodata written within wedges 19, 18. These wedges include servo data 10that are used for control and synchronization of a read/write headassembly over a desired location on storage medium 1. In particular, theservo data generally includes a preamble pattern 11 followed by a servoaddress mark 12 (SAM). Servo address mark 12 is followed by a Gray code13, and Gray code 13 is followed by burst information 14. It should benoted that while two tracks and two wedges are shown, hundreds of eachwould typically be included on a given storage medium. Further, itshould be noted that a servo data set may have two or more fields ofburst information. Yet further, it should be noted that differentinformation may be included in the servo fields such as, for example,repeatable run-out information that may appear after burst information14.

Between the servo data bit patterns 10 a and 10 b, a user data region 16is provided. User data region 16 may include one or more sets of datathat are stored to storage medium 1. The data sets may include usersynchronization information some of which may be used as a mark toestablish a point of reference from which processing of the data withinuser data region 16 may begin processing.

In operation, storage medium 1 is rotated in relation to a sensor thatsenses information from the storage medium. In a read operation, thesensor would sense servo data from wedge 19 (i.e., during a servo dataperiod) followed by user data from a user data region between wedge 19and wedge 18 (i.e., during a user data period) and then servo data fromwedge 18. In a write operation, the sensor would sense servo data fromwedge 19 then write data to the user data region between wedge 19 andwedge 18. Then, the sensor would be switched to sense a remainingportion of the user data region followed by the servo data from wedge18. Once the user data region is reached, a user sync mark 50 isdetected and used as a reference point from which data processing isperformed. User sync mark 50 is preceded by a user preamble 51.

As used herein, the phrase “sync mark” is used in its broadest sense tomean any pattern that may be used to establish a point of reference.Thus, for example, a sync mark may be user sync mark 50 as is known inthe art, or one or more portions of servo data bit patterns 10. Basedupon the disclosure provided herein, one of ordinary skill in the artmay recognize other sync marks that could be used in relation todifferent embodiments of the present invention.

Various embodiments of the present invention provide systems and methodsfor pattern detection. Such systems and methods may be used to, forexample, detect a sync mark pattern or another pattern. The systems andmethods utilize a noise whitened distance measurement to yield acomparison value. The magnitude of the comparison value corresponds towhether a reference signal has been detected or not. Such an approachconsiders noise correlation between proximate bit positions, and noisecancellation is applied using a noise whitening filter. As one of manyadvantages achievable, such noise reduction reduces the possibility offalsely identifying a pattern or failing to properly identify a pattern.

Turning to FIG. 2 a, a noise whitened based pattern detector circuit 200is shown in accordance with one or more embodiments of the presentinvention. Noise whitened based pattern detector circuit 200 includes ananalog to digital converter circuit 210. Analog to digital convertercircuit 210 receives a data input 205. Data input 205 is an analogsignal. In some cases, data input 205 is derived from a storage medium.In other cases, data input 205 is derived from a transmission medium.Based upon the disclosure provided herein, one of ordinary skill in theart will recognize a variety of sources of data input 205. Analog todigital converter circuit 210 samples data input 205 and provides aseries of data samples 215 corresponding to data input 205. Analog todigital circuit 210 may be any circuit known in the art that is capableof converting an analog input signal to a corresponding series ofdigital samples.

Data samples 215 are provided to an equalizer circuit 215. Equalizercircuit 215 may be any circuit known in the art that is capable ofequalizing an input to a target, and providing an equalized output. Insome embodiments, equalizer circuit 210 is a digital finite impulseresponse filter as are known in the art. Based upon the disclosureprovided herein, one of ordinary skill in the art will recognize avariety of equalizer circuits that may be used in relation to differentembodiments of the present invention. Equalizer circuit 220 provides anequalized output 225.

Equalized output 225 is provided to a noise whitened distancecalculation circuit 230. Noise whitened distance calculation circuit 230compares a series of values received as equalized output 225 with areference signal 245. Reference signal 245 may be fixed or programmable,and is provided from a pattern register 240. Where reference signal 245is programmable, pattern register 240 is accessible via a programminginterface (not shown). In some cases, reference signal 245 may be a syncmark pattern indicating the start or end of an information set that isderived either from a storage medium or from a transmission medium.Noise whitened distance calculation circuit 230 performs a bit positionby bit position noise whitened comparison of the received equalizedoutput 225 with reference signal 245. The following equation describesthe operation of noise whitened distance calculation circuit 230:

${{Output} = {\sum\limits_{i = 0}^{l}\left\lbrack {\sum\limits_{k = 0}^{m}{f_{k}\left( {{{equalizer}\mspace{14mu} {output}_{i - k}} - {{reference}\mspace{14mu} {signal}_{i - k}}} \right)}} \right\rbrack^{2}}},$

where an m-tap noise whitening filter is used and f_(k) represents therespective noise whitening filter taps, and l represents the number ofbit positions that are compared (i.e., the number of bit positions inreference signal 245). Of note, the filter taps may be pattern dependent(e.g., tuned for a specific sync mark pattern or the like). In such acase, an index i could represent a bit position and the filter taps foreach I may correspond to bit positions, i, i−1, i−2, i−3 . . . i−x.Noise whitened distance calculation circuit 230 provides the calculatedoutput as a comparison value 235.

Comparison value 235 is provided to a comparator circuit 250 thatcompares comparison value 235 with a threshold value 237. Wherecomparison value 235 is less than threshold value 237, a pattern foundoutput 295 is asserted. Comparator circuit 237 may be any circuit knownin the art capable of comparing two or more signals and providing anoutput indicative of the comparison. Based upon the disclosure providedherein, one of ordinary skill in the art will recognize a variety ofcomparator circuits that may be used in relation to differentembodiments of the present invention. Threshold value 237 may beprogrammable or fixed depending upon the particular implementation. Insome cases, programmable threshold 237 varies based on a feedback signal(not shown). Based upon the disclosure provided herein, one of ordinaryskill in the art will recognize a variety of implementations and/orsources of threshold value 237.

Turning to FIG. 2 b, one implementation of a noise whitened distancecalculation circuit 281 is shown in accordance with some embodiments ofthe present invention. Noise whitened distance calculation circuit 281may be used in place of noise whitened distance calculation circuit 230of FIG. 2 a. Noise whitened distance calculation circuit 281 includes adifference calculation circuit 261 that calculates a bit position by bitposition difference between a received equalized output 225 andreference signal 245 in accordance with the following equation:

Difference_(x)=equalizer output_(x)−reference signal_(x),

where x indicates a given bit position. The difference is provided as anoutput 266 to a difference buffer circuit 271 where the calculateddifference values are stored. The stored difference values are providedas a difference output 276 to a noise whitening filter circuit 211 thatoperates to reduce the noise in any given bit position based upon anexpected interaction with surrounding bits as indicated by m filter taps(f) 203. In particular, noise whitening filter 211 receives an equalizedoutput 201 and provides a noise whitened output 216 in accordance withthe following equation:

${\text{noise~~whitened~~output} = {\sum\limits_{k = 0}^{m}{f_{k}\left( {{{equalizer}\mspace{14mu} {output}_{i - k}} - {{reference}\mspace{14mu} {signal}_{i - k}}} \right)}}},$

where k indicates one of a given noise whitening filter tap (e.g.,f_(k)), and (i−k) indicates a given bit position. Of note, theaforementioned equation may be augmented with a mean subtraction term toremove any deterministic mean from the filter output value. Such a termis optional, but may be advantageous in systems where there issystematic misequalization.

Noise whitened output 216 is provided to a multiplier circuit 221 whereit is squared to yield a squared output 226 in accordance with thefollowing equation:

$\text{squared~~output} = {\left\lbrack {\sum\limits_{k = 0}^{m}{f_{k}\left( {{{equalizer}\mspace{14mu} {output}_{i - k}} - {{reference}\mspace{14mu} {signal}_{i - k}}} \right)}} \right\rbrack^{2}.}$

Squared output 226 is provided to an accumulator circuit 231.Accumulator circuit 231 accumulates the squared output 226 for each bitposition of the corresponding reference signal 245. In particular,accumulator circuit 231 performs an accumulation over l bit positions toyield a comparison output 241 in accordance with the following equation:

$\text{comparison~~output} = {\sum\limits_{i = 0}^{l}{\left\lbrack {\sum\limits_{k = 0}^{m}{f_{k}\left( {{{equalizer}\mspace{14mu} {output}_{i - k}} - {{reference}\mspace{14mu} {signal}_{i - k}}} \right)}} \right\rbrack^{2}.}}$

Turning to FIG. 3, a flow diagram 300 shows a method for identifying apattern in accordance with one or more embodiments of the presentinvention. Following flow diagram 300, data samples are received as adata input (block 305). The received data input may be derived from, forexample, a storage medium or a communication medium. Based upon thedisclosure provided herein, one of ordinary skill in the art willrecognize a variety of sources of the data input. An analog to digitalconversion is performed on the data input to yield a data samplecorresponding to a particular bit position (block 310). The analog todigital conversion may be performed using any analog to digitalconversion circuit or approach known in the art. An equalization isperformed on the digital sample to yield an equalized samplecorresponding to the bit position (block 315). The equalization may bedone using any equalizer circuit or equalization method known in theart.

For each bit position of a reference signal, a difference between thereference signal and a corresponding equalized sample is calculated(block 325). As an example, the difference calculation may be done inaccordance with the following equation:

Difference_(x)=equalizer output_(x)−reference signal_(x),

where x indicates a given bit position. Noise whitening filtering isapplied to a set of difference values to yield a set of noise whitenedoutputs (block 330). Such noise whitening filtering may be done inaccordance with the following equation:

${{\text{noise~~whitened~~}{output}_{i}} = {\sum\limits_{k = 0}^{m}{f_{k}\left( {Difference}_{i - k} \right)}}},$

where k indicates one of a given noise whitening filter tap (e.g.,f_(k)), (i−k) indicates a given bit position, and i represents a noisewhitened output for a given bit position. Of note, the filter taps maybe pattern dependent (e.g., tuned for a specific sync mark pattern orthe like). In such a case, an index i could represent a bit position andthe filter taps for each I may correspond to bit positions, i, i−1, i−2,i−3 . . . i−x. Also, it should be noted that the aforementioned equationmay be augmented with a mean subtraction term to remove anydeterministic mean from the filter output value. Such a term isoptional, but may be advantageous in systems where there is systematicmisequalization.

Each of the noise whitened outputs are squared to yield a squared output(block 335). Such squaring may be done in accordance with the followingequation:

squared output_(i)=(noise whitened output_(i))².

Each of the squared outputs corresponding to the bit positions ofreference signal are summed to yield a comparison value (block 340). Thecomparison value may be calculated in accordance with the followingequation:

${\text{comparison~~value} = {\sum\limits_{i = 0}^{l}{{squared}\mspace{14mu} {output}_{i}}}},$

where l corresponds to the number of bit positions in the referencesignal. This comparison value is compared with a threshold value (block345). Where the comparison value is less than the threshold value (block350), a pattern found is indicated (block 360). In either case, theprocesses are repeated for the next received data input.

Turning to FIG. 4, a communication system 400 including a receiver 420with a noise whitened based pattern detector circuit is shown inaccordance with different embodiments of the present invention.Communication system 400 includes a transmitter 410 that is operable totransmit encoded information via a transfer medium 430 as is known inthe art. The encoded data is received from transfer medium 430 byreceiver 420. Receiver 420 incorporates a noise whitened based patterndetector circuit. The noise whitened based pattern detector circuit maybe similar to that discussed above in relation to one or more ofrelation to FIGS. 2 a and 2 b, and/or may operate in accordance with themethod discussed above in relation to FIG. 3.

Turning to FIG. 5, a storage system 500 including a read channel circuit510 with a non-threshold based sync mark detector circuit is shown inaccordance with various embodiments of the present invention. Storagesystem 500 may be, for example, a hard disk drive. Storage system 500also includes a preamplifier 570, an interface controller 520, a harddisk controller 566, a motor controller 568, a spindle motor 572, a diskplatter 578, and a read/write head 576. Interface controller 520controls addressing and timing of data to/from disk platter 578. Thedata on disk platter 578 consists of groups of magnetic signals that maybe detected by read/write head assembly 576 when the assembly isproperly positioned over disk platter 578. In one embodiment, diskplatter 578 includes magnetic signals recorded in accordance with eithera longitudinal or a perpendicular recording scheme.

In a typical read operation, read/write head assembly 576 is accuratelypositioned by motor controller 568 over a desired data track on diskplatter 578. Motor controller 568 both positions read/write headassembly 576 in relation to disk platter 578 and drives spindle motor572 by moving read/write head assembly to the proper data track on diskplatter 578 under the direction of hard disk controller 566. Spindlemotor 572 spins disk platter 578 at a determined spin rate (RPMs). Onceread/write head assembly 578 is positioned adjacent the proper datatrack, magnetic signals representing data on disk platter 578 are sensedby read/write head assembly 576 as disk platter 578 is rotated byspindle motor 572. The sensed magnetic signals are provided as acontinuous, minute analog signal representative of the magnetic data ondisk platter 578. This minute analog signal is transferred fromread/write head assembly 576 to read channel module 564 via preamplifier570. Preamplifier 570 is operable to amplify the minute analog signalsaccessed from disk platter 578. In turn, read channel circuit 510decodes and digitizes the received analog signal to recreate theinformation originally written to disk platter 578. This data isprovided as read data 503 to a receiving circuit. As part of decodingthe received information, read channel circuit 510 performs a sync markdetection process. Such a sync mark detection process may be performedusing a sync mark detector circuit that may be similar to one or more ofthose discussed above in relation to FIGS. 2 a and 2 b. The sync markdetection process may be done in accordance with the method discussedabove in relation to FIG. 3. A write operation is substantially theopposite of the preceding read operation with write data 501 beingprovided to read channel circuit 510. This data is then encoded andwritten to disk platter 578.

It should be noted that storage system 500 may be integrated into alarger storage system such as, for example, a RAID (redundant array ofinexpensive disks or redundant array of independent disks) based storagesystem. It should also be noted that various functions or blocks ofstorage system 500 may be implemented in either software or firmware,while other functions or blocks are implemented in hardware.

It should be noted that the various blocks discussed in the aboveapplication may be implemented in integrated circuits along with otherfunctionality. Such integrated circuits may include all of the functionsof a given block, system or circuit, or only a subset of the block,system or circuit. Further, elements of the blocks, systems or circuitsmay be implemented across multiple integrated circuits. Such integratedcircuits may be any type of integrated circuit known in the artincluding, but are not limited to, a monolithic integrated circuit, aflip chip integrated circuit, a multichip module integrated circuit,and/or a mixed signal integrated circuit. It should also be noted thatvarious functions of the blocks, systems or circuits discussed hereinmay be implemented in either software or firmware. In some such cases,the entire system, block or circuit may be implemented using itssoftware or firmware equivalent. In other cases, the one part of a givensystem, block or circuit may be implemented in software or firmware,while other parts are implemented in hardware.

In conclusion, the invention provides novel systems, devices, methodsand arrangements for data processing. While detailed descriptions of oneor more embodiments of the invention have been given above, variousalternatives, modifications, and equivalents will be apparent to thoseskilled in the art without varying from the spirit of the invention.Therefore, the above description should not be taken as limiting thescope of the invention, which is defined by the appended claims.

1. A pattern detection circuit, the circuit comprising: a distancecalculation circuit operable to calculate a noise whitened distancebetween a reference signal and a received input to yield a comparisonvalue; and a comparator circuit operable to compare the comparison valuewith a threshold value.
 2. The circuit of claim 1, wherein thecomparator circuit is further operable to assert a pattern found signalwhen the comparison value is less than the threshold value.
 3. Thecircuit of claim 1, wherein the distance calculation circuit includes: adifference circuit operable to calculate a difference between thereference signal and the received input at a bit position to yield adifference value; and a noise whitening filter operable to noise whitenthe difference value to yield a noise whitened output.
 4. The circuit ofclaim 3, wherein the distance calculation circuit further includes: amultiplier circuit operable to square the noise whitened output to yielda squared output.
 5. The circuit of claim 4, wherein the bit position isa first bit position, wherein the difference value is a first differencevalue, wherein the noise whitened output is a first noise whitenedoutput, wherein the squared output is a first squared output, andwherein: the difference circuit is further operable to calculate adifference between the reference signal and the received input at asecond bit position to yield a second difference value; the noisewhitening filter is further operable to noise whiten the seconddifference value to yield a second noise whitened output; the multipliercircuit is operable to square the second noise whitened output to yielda second squared output; and an accumulator circuit operable to sum atleast the first squared output and the second squared output to yieldthe comparison value.
 6. The circuit of claim 1, wherein the circuitfurther comprises: a pattern register operable to maintain the referencesignal.
 7. The circuit of claim 6, wherein the pattern register isprogrammable.
 8. The circuit of claim 1, wherein the comparison value iscalculated in accordance with the following equation:${\text{comparison~~output} = {\sum\limits_{i = 0}^{l}\left\lbrack {\sum\limits_{k = 0}^{m}{f_{k}\left( {{{received}\mspace{14mu} {input}_{i - k}} - {{defined}\mspace{14mu} {signal}_{i - k}}} \right)}} \right\rbrack^{2}}},$wherein l corresponds to the number of bit positions of the referencesignal, m corresponds to the number of taps of a noise whitening filter,i−k corresponds to a particular bit position, and f_(k) represents aparticular tap of the noise whitening filter.
 9. The circuit of claim 1,wherein the circuit is implemented in an integrated circuit.
 10. Thecircuit of claim 1, wherein the circuit is implemented as part of adevice selected from a group consisting of: a storage device, and acommunication device.
 11. A method for pattern detection, the methodcomprising: receiving a data input; receiving a reference signal;calculating a difference between the reference signal and the receivedinput at a bit position to yield a difference value; noise whitening thedifference value to yield a noise whitened output; and calculating adistance between the data input and the reference signal based at leastin part on the noise whitened output to yield a comparison value. 12.The method of claim 11, wherein calculating the distance between thedata input and the reference signal based at least in part on the noisewhitened output includes: squaring the noise whitened output to yield asquared output, wherein the comparison value is calculated based atleast in part on the squared output.
 13. The method of claim 11, whereinthe bit position is a first bit position, wherein the difference valueis a first difference value, wherein the noise whitened output is afirst noise whitened output, and wherein the method further comprises:calculating a difference between the reference signal and the receivedinput at a second bit position to yield a second difference value; noisewhitening the second difference value to yield a second noise whitenedoutput; squaring the first noise whitened output to yield a firstsquared output; squaring the second noise whitened output to yield asecond squared output; and summing at least the first squared output andthe second squared output to yield the comparison value.
 14. The methodof claim 13, wherein: calculating the difference between the referencesignal and the received input is done in accordance with the followingequation:Difference_(x)=received input_(x)−defined pattern_(x), wherein xindicates a given bit position; noise whitening the difference value isdone in accordance with the following equation:${{\text{noise~~whitened~~}{output}} = {\sum\limits_{k = 0}^{m}{f_{k}\left( {Difference}_{k - m} \right)}}},$wherein k indicates one of a given noise whitening filter tap, f_(k) isthe filter tap value, and (k−m) indicates a given bit position; squaringthe noise whitened output is done in accordance with the followingequation:squared output_(i)=(noise whitened output_(i))², wherein i indicates abit position; and summing at least the first squared output and thesecond squared output to yield the comparison value is done inaccordance with the following equation:$\text{comparison~~value} = {\sum\limits_{i = 0}^{l}{{squared}\mspace{14mu} {{output}_{i}.}}}$15. The method of claim 11, wherein the method further comprises:comparing the comparison value with a threshold value; and asserting apattern found signal based at least in part on the comparison betweenthe comparison value and the threshold value.
 16. The method of claim11, wherein noise whitening the difference value to yield a noisewhitened output is done in accordance with the following equation:${{\text{noise~~whitened~~}{output}} = {\sum\limits_{k = 0}^{m}{f_{k}\left( {Difference}_{k - m} \right)}}},$wherein k indicates one of a given noise whitening filter tap, f_(k) isthe filter tap value, and (k−m) indicates a given bit position.
 17. Themethod of claim 11, wherein calculating the difference between thereference signal and the received input at a bit position to yield adifference value is done in accordance with the following equation:Difference_(x)=received input_(x)−defined pattern_(x), wherein xindicates a given bit position.
 18. A storage device, the storage devicecomprising: a storage medium; a read/write head assembly disposed inrelation to the storage medium and operable to derive a data input fromthe storage medium; an analog to digital converter circuit operable toconvert the data input to a series of digital samples; an equalizercircuit operable to equalize the series of data samples to yield anequalized output; a distance calculation circuit operable to calculate anoise whitened distance between a reference signal and the equalizedoutput to yield a comparison value; and a comparator circuit operable tocompare the comparison value with a threshold value.
 19. The storagedevice of claim 18, wherein the distance calculation circuit includes: adifference circuit operable to calculate a difference between thereference signal and the received input at a bit position to yield adifference value; a noise whitening filter operable to noise whiten thedifference value to yield a noise whitened output; and a multipliercircuit operable to square the noise whitened output to yield a squaredoutput.
 20. The storage device of claim 19, the difference value is afirst difference value corresponding to a first bit position; whereinthe noise whitened output is a first noise whitened output, wherein thesquared output is a first squared output, and wherein: the differencecircuit is further operable to calculate a difference between thereference signal and the received input at a second bit position toyield a second difference value; the noise whitening filter is furtheroperable to noise whiten the second difference value to yield a secondnoise whitened output; the multiplier circuit is operable to square thesecond noise whitened output to yield a second squared output; and anaccumulator circuit operable to sum at least the first squared outputand the second squared output to yield the comparison value.